## Area of a Rectangle

In geometry, the concept of area in a two-dimensional or three-dimensional figure helps us find the amount of space occupied by them. For example, for the given rectangle, the amount of color required to fill the rectangle can be found by determining its area.

Likewise, we can calculate the space occupied by a rectangular lawn in a park by finding the area of its rectangle shape.

We can find the area of any two-dimensional shape by dividing that shape into smaller unit squares. Since each unit square occupies one square unit space, the total number of unit squares in the shape gives its area. The area of a shape is measured in square units.

Consider a rectangle of length 6 in. and width 3 in. It can be filled with 3 rows and 6 columns of unit squares.

Each of these squares has an area of 1 square inch, and in the rectangle, there are 18 such squares. So, the area of the rectangle is 18 square inches. We could also have determined this area by simply multiplying the length and width of the rectangle.

In other words, the area of a rectangle is the product of its length and width.

## The Formula for Finding the Area of a Rectangle

The formula for the area of a rectangle is shown below:

Area of a rectangle = length (l) ✕ width (w)

**For example**,

the area of a rectangle of length 35 m and width 25 m is 35 times 25 or 875 square meters.

**Fun Facts**

– The square is a special type of rectangle whose length and width are the same. Hence, the area of a square is given by multiplying the length of each side by itself.

## Solved Examples

**Q1- Calculate the area of a rectangle with a width of 5 cm and a length of 20 cm.**

**Solution:**

Given,

Width (w) = 5 cm, Length (l) = 20 cm

Area of a rectangle = l ✕ w = 20 × 5 = 100

Hence, area = 100 cm^{2}

**Q2 – What is the area of a rectangular table in m**^{2}^{ }**with a length of 130 cm and a width of 110 cm?**

**Solution:**

Length of the table = l = 130 cm or 1.3 m

width of the table = w = 110 cm or 1.1 m

Area of the rectangular table = l ✕ w = 1.3 m x 1.1 m = 1.43 square-meters (m^{2})

**Q3 – A rectangular window measures 25 cm in length. It has a 100 cm**^{2}** area. Determine the width of the window.**

**Solution:**

Area of the window = 100 cm^{2}

Length of the window = l = 25 cm

Area of a rectangle = l ✕ w

100 = 25 ✕ w

Thus, width of the window = $\frac{100}{25}$ = 4 cm

**Q4. **A rectangular room has a length of 12 feet and a width of 14 feet. How much carpet is required to cover the entire room?

The area of the carpet is equal to the area of the room.

We can find the area of the room by multiplying its length by width.

Area of carpet = length ✕ width

Area of carpet = 12 ✕ 14 = 168 square feet.

Therefore, to cover the room, 168 square feet of carpet is required.

## Practice Problems

## Area of a Rectangle

### Find the area of a rectangle whose length is 20 cm and width is 4 cm.

Area = 20 cm ✕ 4 cm = 80 cm

^{2}

### A rectangular blackboard has a width of 130 cm and a height of 90 cm. Find the area of this blackboard.

^{2}

^{2}

^{2}

^{2}

^{2}

90 cm ✕ 130 cm = 11,700 cm

^{2}

### A wall whose length and width are 10 m and 30 m, respectively, has to be covered by marble blocks. The dimension of the blocks is 2 m × 1 m. Find the total number of blocks needed to fully cover the wall.

Area of wall = 10 ✕ 30 = 300 sq.m.

Area of 1 block = 2 ✕ 1 = 2 sq.m.

Total number of blocks required to fully cover the wall = $\frac{300}{2}$ =150

### A rectangular wall measures 15 m in length and 20 m in width. Calculate the price of coloring the wall at the rate of $\$1.2$ per m^{2}.

Cost of coloring the wall = $\$1.2$ ✕ 15 x 20 = $\$360$

## Frequently Asked Questions

**What is the formula for calculating the area of a rectangle?**

The formula for calculating the area of a rectangle is length times the width.

**How do you find the length of the rectangle given area and width?**

Firstly, we know the formula for calculating the area of a rectangle is, area = length ✕ width. We can find the length by transposing width to the other side of the equation. <br>

Therefore, length = $\frac{area}{width}$

**What is the formula for calculating the area of a square?**

The square is a special type of rectangle whose length and width are the same. Hence, the area of a square is given by multiplying the length of each side by itself. <br>

Area of square = side ✕ side.